The question consists of four statements numbered “I,

Solution

Let the investment of ‘A’ = Rs. ‘X’ Then, investment of ‘B’ = Rs. (X + 1800) Let the time period of investment of ‘A’ = ‘y’ months Then, time period of investment of ‘B’ = (y – 5) months Statement I: We have, y = 10 So, ratio of profit shares of ‘A’ and ‘B’ = (X × 10):{(X + 1800) × (10 – 5)} = 10X:(5X + 9000) But we cannot proceed any further with this and we cannot determine the profit share of ‘B’. So, data in statement I alone is not sufficient to answer the question. Statement II: Reduced investment of ‘B’ = X + 1800 – 600 = Rs. (X + 1200) Ratio of profit shares of ‘A’ and ‘B’ respectively = (X × y):{(X + 1200) × (y – 5)} Or, Xy:{Xy + 1200y – 5X – 6000} According to the statement, Xy = 1.25 × (Xy + 1200y – 5X – 6000) Or, Xy = 1.25Xy + 1500y – 6.25X – 7500 Or, 0.25Xy + 1500y – 6.25X – 7500 = 0 Since this equation cannot be solved any further, we cannot determine the profit share of ‘B’. So, data in statement II alone is not sufficient to answer the question. Statement III: Let the investments of ‘A’ and ‘B’ be Rs. ‘3x’ and Rs. ‘5x’, respectively. Then, according to the statement, (3x × y):{5x × (y – 5 + 3)} = 3:4 Or, 3xy:{5x × (y – 2)} = 3:4 Or, 3xy:(5xy – 10x) = 3:4 Or, (3xy/3) = (5xy – 10x) ÷ 4 Or, 4xy = 5xy – 10x So, y = 10 So, ratio of actual profit shares of ‘A’ and ‘B’ = (3x × 10):{5x × (10 – 5)} = 30x:25x = 6:5 So, profit share of ‘B’ = 8800 × (5/11) = Rs. 4,000 So, data in statement III alone is sufficient to answer the question. Statement IV: Since ‘A’ has invested for 10 months, so time period of investment of ‘B’ = 10 – 5 = 5 months Investment of ‘B’ = 2700 + 1800 = Rs. 4,500 So, ratio of profit shares of ‘A’ and ‘B’ respectively = (2700 × 10):(4500 × 5) = 27000:22500 = 6:5 So, let the profit shares of ‘A’ and ‘B’ be Rs. 6k and Rs. 5k, respectively. We have, 6k – 5k = 800 Or, k = 800 So, profit share of ‘B’ = 5k = 800 × 5 = Rs. 4,000 So, data in statement IV alone is sufficient to answer the question. Hence, option C.